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Open AccessArticle

Remarks on the Preservation of the Almost Fixed Point Property Involving Several Types of Digitizations

Department of Mathematics Education, Institute of Pure and Applied Mathematics, Jeonbuk National University, Jeonju 54896, Korea
Mathematics 2019, 7(10), 954; https://doi.org/10.3390/math7100954
Received: 2 September 2019 / Revised: 30 September 2019 / Accepted: 8 October 2019 / Published: 12 October 2019
(This article belongs to the Special Issue Fixed Point Theory and Related Nonlinear Problems with Applications)
This paper explores a certain relationship between the almost fixed point property (AFPP for short) of a compact and n-dimensional Euclidean space and that of its digitized space. Based on several types of digitizations, we prove that the AFPP of a compact and n-dimensional Euclidean cube is preserved by each of the U ( k ) , the L ( k ) and the Khalimsky digitizations, k 3 n - 1 , n N .
Keywords: digital space; U-and L-digitization; fixed point property; almost fixed point property; Khalimsky topology; digital topology digital space; U-and L-digitization; fixed point property; almost fixed point property; Khalimsky topology; digital topology
MDPI and ACS Style

Han, S.-E. Remarks on the Preservation of the Almost Fixed Point Property Involving Several Types of Digitizations. Mathematics 2019, 7, 954.

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